Finite Group Databasebeta

← #34043673

Subgroups — #34043673

Order 19072.

260 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 260 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#23750213C211yesmaximal, characteristic
2#23749783C211yesmaximal, characteristic, complemented
3#23749766C211yesmaximal, characteristic, complemented
4#23749537C211yesmaximal, characteristic, complemented
5#23749363C211yesmaximal, characteristic, complemented
6#23749360C211yesmaximal, characteristic, complemented
7#323×C149C211yesmaximal, characteristic, complemented
8C22×Dic298C2211yescharacteristic
9C2×Dic596—21no—
10C2×#14558725—21no—
11#18011904—21no—
12#18011897—21no—
13#18011893—21no—
14#18011890C2211yescharacteristic
15#18011885C2211yescharacteristic
16#18011884—21no—
17#18011880—21no—
18C4×C22⋊D149—21no—
19C2×C22⋊Dic149—21no—
20#18011836—21no—
21#18011836—21no—
22#18011818—21no—
23#18011818C2211yescharacteristic
24C2×C22⋊C4×C149C2211yescharacteristic
25C22⋊C8×C149C2211yescharacteristic
26C22⋊C8×C149C2211yescharacteristic
27C2×Dic298—21no—
28C2×Dic298—21no—
29C2×Dic298—42no—
30C2×Dic298D411yescharacteristic
31C2×D596D411yescharacteristic
32C2×C22⋊D149—21no—
33C2×C22⋊D149—21no—
34C2×C22⋊D149—21no—
35C22×Dic149—21no—
36C22×Dic149—21no—
37C2×C4×D149—21no—
38Dic596—42no—
39#14558725—42no—
40C4⋊Dic149D411yescharacteristic
41C4⋊Dic149D411yescharacteristic
42#14558715—21no—
43#14558715—21no—
44C22⋊Dic149—21no—
45C22⋊Dic149—21no—
46C22⋊Dic149—21no—
47C22⋊Dic149—42no—
48#14558713—21no—
49#14558713—21no—
50C4×Dic149—21no—
51C24×C149D411yescharacteristic
52C22×C4×C149D411yescharacteristic
53C22×C4×C149C2311yescharacteristic
54C2×C8×C149—21no—
55C2×C8×C149—21no—
56C22⋊C4×C149—21no—
57C22⋊C4×C149—21no—
58C22×D149—21no—
59Dic298—22no—
60Dic298—22no—
61Dic298—41no—
62Dic298—41no—
63Dic298—41no—
64D596—41no—
65C22⋊D149—41no—
66C22⋊D149—41no—
67C22⋊D149—81no—
68C22⋊D149—81no—
69C2×Dic149—22no—
70C2×Dic149—21no—
71C2×Dic149—21no—
72C2×Dic149—21no—
73C2×Dic149—41no—
74C2×Dic149—41no—
75C2×Dic149—41no—
76C2×Dic149—41no—
77C2×Dic149—41no—
78C4×D149—81no—
79C23×C149—21no—
80C23×C149—21no—
81C23×C149—21no—
82C23×C149—41no—
83C23×C149—41no—
84C23×C149C2×D411yescharacteristic
85C2×C4×C149—21no—
86C2×C4×C149—41no—
87C2×C4×C149—41no—
88C2×C4×C149C2×D411yescharacteristic
89C2×C4×C149C2×D411yescharacteristic
90C8×C149—41no—
91C8×C149—41no—
92C22×C149—21no—
93C22×C149—21no—
94C22×C149—42no—
95C22×C149—41no—
96C22×C149—41no—
97C22×C149—41no—
98C22×C149—81no—
99C22×C149#12011yescharacteristic
100C22×C149#13511yescharacteristic
101C22×C149#13711yescharacteristic
102C2×D149—41no—
103C2×D149—41no—
104C2×D149—41no—
105C4×C149—21no—
106C4×C149—21no—
107C4×C149—41no—
108Dic149—41no—
109Dic149—41no—
110Dic149—42no—
111Dic149—41no—
112Dic149—81no—
113C2×C149—21no—
114C2×C149—21no—
115C2×C149—81no—
116C2×C149#45211yescharacteristic
117C2×C149#45511yescharacteristic
118C2×C149B(4,𝔽2)11yescharacteristic
119D149—81no—
120C149#160611yescharacteristic, complemented, Sylow
121#1606—1491nomaximal, Sylow
122#538—1491no—
123#451—1491no—
124#448—1491no—
125#393—1491no—
126#328—1491no—
127#327—1491no—
128#323D14911yescharacteristic, complemented
129C22×Q8—1491no—
130C2×Q16—2981no—
131C2×SD16—2981no—
132#126—2981no—
133#124—2981no—
134#123—2981no—
135C22⋊Q8—1491no—
136#121—2981no—
137#121—1491no—
138#120—2981no—
139C4×D4—2981no—
140C2×C22⋊C4—2981no—
141C2×C22⋊C4C2×D14911yescharacteristic
142#103—2981no—
143#103—2981no—
144C22⋊C8C2×D14911yescharacteristic
145C22⋊C8C2×D14911yescharacteristic
146#95—2981no—
147#95—1491no—
148C24D59611yescharacteristic
149C2×Q8—2981no—
150C2×Q8—2981no—
151C2×Q8—5962no—
152C2×Q8—1491no—
153C2×D4—2981no—
154C2×D4—2981no—
155C2×D4—2981no—
156C2×D4—1491no—
157C22×C4—2981no—
158C22×C4—2981no—
159C22×C4—2981no—
160C22×C4D59611yescharacteristic
161C22×C4C22×D14911yescharacteristic
162Q16—5962no—
163SD16—5962no—
164C2×C8—21no—
165C2×C8—21no—
166C4⋊C4—2981no—
167C4⋊C4—2981no—
168C4⋊C4—1491no—
169C4⋊C4—1491no—
170C22⋊C4—21no—
171C22⋊C4—21no—
172C22⋊C4—2981no—
173C22⋊C4—2981no—
174C22⋊C4—2981no—
175C22⋊C4—2981no—
176C22⋊C4—2981no—
177C22⋊C4—5962no—
178C42—2981no—
179C23—21no—
180C23—21no—
181C23—21no—
182C23—41no—
183C23—41no—
184C23—2981no—
185C23C2×D59611yescharacteristic
186Q8—2982no—
187Q8—2982no—
188Q8—5961no—
189Q8—5961no—
190Q8—5961no—
191D4—5961no—
192D4—5961no—
193D4—5961no—
194D4—11921no—
195D4—11921no—
196C2×C4—21no—
197C2×C4—41no—
198C2×C4—41no—
199C2×C4—2982no—
200C2×C4—2981no—
201C2×C4—2981no—
202C2×C4—2981no—
203C2×C4—5961no—
204C2×C4—5961no—
205C2×C4—5961no—
206C2×C4—5961no—
207C2×C4—5961no—
208C2×C4—11921no—
209C2×C4D4×D14911yescharacteristic
210C2×C4D4×D14911yescharacteristic
211C8—41no—
212C8—41no—
213C22—21no—
214C22—21no—
215C22—42no—
216C22—41no—
217C22—41no—
218C22—41no—
219C22—81no—
220C22—5961no—
221C22—5961no—
222C22—5961no—
223C22#1801188111yescharacteristic
224C22#1801193311yescharacteristic
225C22#1801194411yescharacteristic
226C4—21no—
227C4—21no—
228C4—41no—
229C4—5961no—
230C4—5961no—
231C4—5962no—
232C4—5961no—
233C4—11921no—
234C2—21no—
235C2—21no—
236C2—81no—
237C2—11921no—
238C2#2374978911yescharacteristic
239C2#2374980511yescharacteristic
240C2#2374981311yescharacteristic
subgroupG/H
centerC22#18011881
commutator, cosocleC22×C4×C149C23
FrattiniC22×C4C22×D149
Fitting#323×C149C2
socleC22×C149#120
prime radical#23750213C2
hypercenter#323D149
hypocenterC149#1606
LCSG ▷ C22×C4×C149 ▷ C22×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ #323

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
2. #23749783C2semidirect
3. #23749766C2semidirect
4. #23749537C2semidirect
5. #23749363C2semidirect
6. #23749360C2semidirect
7. #323×C149C2semidirect
120. C149#1606semidirect
128. #323D149semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#237502132
#237497832
#237497662
#237495372
#237493632
#237493602
#323×C1492
#1606149